JOURNAL OF POLYMER SCIENCE: PART A-1 VOL. 7, 471-477 (1969)

Reactivity Ratios for Copolymerization of Vinyl Chloride with 8-Methylpentyl Vinyl Brassylate

by Computerized Linearization*

SHU-PEI CHANG, THOMAS K. MIWA, and WILLIAM H. TALLENT, Northern Regional Research Laboratory, Northern Utilization

Research and Development Division, Agricultural Research Service, United States Department of Agriculture, Peoria, Illinois 61 604

Synopsis A computerized version of the Fineman-Ross linearization procedure was used to

determine reactivity ratios for copolymerization of vinyl chloride (monomer 1) and Zmethylpentyl vinyl brassylate (monomer 2). From differential refractometry data for the products of low-conversion copolymerization, the procedure gave rl = 1.06 and 52 = 0.234. The ratios computed from chlorine contents of the same products were 71 = 1.10 and r~ = 0.239. The polarity factor (e,) and general monomer reactivity (Q2) calculated for monomer 2 from these ratios were, respectively, -0.95 to -0.98 and 0.032-0.033. The interquartile range for the copolymerization of a mixture of 60% monomer 1 and 40% monomer 2 was 1.4%. These values suggest that from suitable proportions of reactants, sufficiently homogeneous distribution of monomers can be achieved in copolymers of vinyl chloride and Zmethylpentyl vinyl brassylate to cffer the possibility of effective internal plasticization.

Introduction

Alkyl vinyl brassylates (AVB) have been prepared from brassylic (tridecanedioic) acid by half-esterification followed by vinylation as shown in the following reaction sequence.'

COOH COOR COOR I ROH I G H z I

(CH2)a 4 (CH2)n - (CH2)ii I I I COOH COOH COOCH=CHz

Three such mixed esters (R = ethyl, 2-methylpentyl, or nonyl) were synthesized as potential internal plasticizers in copolymers with vinyl chloride (VC), and the 2-methylpentyl vinyl brassylate (MVB) has already been tested for this purpose.2

The distribution of comonomers in the VC-AVB copolymers, which can be predicted from reactivity ratios (rl, r2)13 is expected markedly to affect

* Presented at the American Chemical Society Meeting, Division of Polymer Chem- istry, San Francisco, California, March 31-April 5, 1968.

471

472 S.-P. CHANG, T. K. MIWA, W. H. TALLENT

the internal plasticization. The determination of rl and r2 for the VC- MVB system is reported in this paper. Also, the convenience of differential refractometry for finding copolymer composition and a computerized ver- sion of the Fineman-Ross linearization procedure to calculate reactivity ratios are illustrated.

Experimental

MVB was purified by two passes through an ASCO 50 Rota-Film molecu- lar still to remove all of the lower boiling divinyl ester and part of the high boiling, inert dialkyl ester. The purity was 92.3y0 MVB, as determined by gas-liquid chromatography, with absence of polymer being verified by thin-layer chromatography (TLC).' Benzoyl peroxide (Matheson), tetra- hydrofuran (Mallinckrodt, analytical reagent), and VC (Matheson) were used as received.

Copolymerizations of monomer mixtures in 5.0 ml of benzene in the presence of 0.03 g of benzoyl peroxide were carried out in capped, glass pressure tubes. These were mechanically tumbled in a water bath at 60°C for 3 hr to give conversions to copolymer of 8% or less. The reactions were stopped by immersing the tubes in Dry Ice-acetone. The Teflon-gasketed caps were removed, and unreacted VC evaporated as the contents of the tubes slowly warmed to room temperature. The benzene was removed in a rotary evaporator, and the unreacted MVB was removed by 10 washings with methanol. After the last washing, complete removal of monomers was verified by TLC, ' and residual methanol was evaporated under vacuum at 38°C for 57 hr. Homopolymers of VC and MVB were prepared in the same manner except the reaction time was 336 hr.

Refractometric measurements were taken at 20°C with a Waters Model 43 differential refractometer equipped with a 10-in. Honeywell recorder. The reference and sample cells were filled and a baseline was established before the solvent in the sample cell was replaced with polymer solution in tetrahydrofuran. Pen displacement from the baseline was directly pro- portional to the concentration of the solution and was determined for several concentrations ranging from 3 to 12 mg/ml for each sample investigated. The displacement per unit concentration used in subsequent calculations was the average result of the several measurements for each sample.

Benzene was distilled before use.

Chlorine analyses were performed by the method of White.4

Calculations

The specific refractive increment for a binary copolymer is given by the equation:5

v12 = 51v1 + (1 - Z1)VZ (1)

where v1, v2, and v12 are the refractive increments of, respectively, the homo- polymer from monomer 1, the homopolymer from monomer 2, and the copolymer. The quantity x1 is the weight fraction of the monomer 1 in the

REACTIVITY RATIOS 473

copolymer. The Waters differential refractometer gives a recorder pen displacement proportional to the differential refractive index, and the values calculated by dividing the pen displacements (in inches) by concentration (in milligrams per millileter) can be used in eq. (1). The value so obtained for poly(viny1 chloride) (PVC) was 7.90 from an average of results for three samples: 7.93 for the benzoyl peroxide-initiated homopolymer prepared as described above, 7.89 for a PVC sample prepared by 0.3% potassium persulfate-initiated polymerization,2 and 7.89 for B. F. Goodrich Geon 101. Averaging results (4.38 and 4.35) of two sets of measurements for MVB homopolymer gave 4.37. Substituting in eq. (1) and rearranging we may write:

21 = (Diz - 4.37)/(7.90 - 4.37) (2) where Dl2 is the differential refractometer recorder pen displacement per unit concentration for the copolymer.

From the Mayo-Lewis copolymerization equation,6 Fineman and Ross’ derived a pair of linear equations:

F is the molar ratio of monomer 1 to monomer 2 in the original mixture, and f i s the analogous ratio in the corresponding copolymer. Our computer pro- gram, which utilizes eqs. (3) and (4), accepts as input either weights of monomers in the initial mixture and compositional data on the copolymers produced or molar ratios calculated from such data. The quantities F and f are first computed from the input. Then the lines which fit eqs. (3) and (4) best are determined by the linear least-squares treatment* of the experi- mental data. Reactivity ratios determined from the slope and intercept of each of the two equations are shown on the printout, but values of r1 re- ported here as calculated by the linear least-squares method were deter- mined from eq. (3), and the corresponding values of r2 were determined from eq. (4). The program also includes instruction cards necessary for calculation of the polarity factor (ez) and general monomer reactivity (Qz) for monomer 2. Copies of the program, which is written in Fortran IV language for an IBM 1130 computer and comprises approximately 100 cards, are available upon request.

The quantities ez and Qz for MVB were calculated from eqs. (5 ) and (6).s To substitute for the corresponding VC constants in the equations,

we selected the averaged values reported by Young;’O namely, el = 0.20 and@ = 0.044.

The relationship between instantaneous copolymer composition and percentage conversion was determined either by graphic solution of the

474 S.-P. CHANG, T. K. MIWA, W. H. TALLENT

Skeist equation1' or by substitution of reactivity ratios into the Meyer- Lowry12 solution. The values of r1 and rz used for this purpose were averages of the two values computed, respectively, from differential refrac- tometry and chlorine analysis data.

Results and Discussion

The determination of composition of copolymers by differential refrac- tometry was first reported by Kinsinger et aL5 and later by Urwin and Stearne13 and was discussed by H~g1in. l~ The general availability of differential refractometers as quantitative detectors on gel-permeation chromatographic units makes this technique very attractive. The results we obtained by this technique were checked by the conventional chlorine analysis. Reactivity ratios computed by the linear least-squares method from data obtained by the two different analytical methods (Table I) are given in Table 11. Even though the agreement is quite good, the difference

TABLE I Copolymerization of Vinyl Chloride (VC) with 2-Methylpentyl

Vinyl Brassylate (MVB)

VC in copolymer, wt-%

Conversion, Differential Chlorine vc, g MVB, g % refractometry analysis

Charges

0.1013 9.8966 2.0 2.97 3.10 0.1433 9.8432 3.5 5.79 5.52 1.1361 8.8626 4.5 21.62 21.38 5.1211 4.8721 5.8 55.82 54.95 6.3987 3.6001 7.3 66.56 66.95 7.9121 2.1131 8.4 80.41 81.07

a With 0.03 g of benzoyl peroxide as initiator and 5 ml of benzene as solvent.

TABLE I1 Reactivity Ratios and e and Q Values for the Copolymerization of Vinyl

Chloride (Monomer 1) and ZMethylpentyl Vinyl Brassylate (Monomer 2).

Method r1 r!2 e2 Q2

Differential refractometry 1.06 0.234 -0.98 0.033 Chlorine analysis 1.10 0.239 -0.95 0.032

Corresponding values for VC are taken from Younglo as el = 0.20 and Q1 = 0.044.

between rl values being less than 4% and that between r2 values only about 2%, we investigated one probable cause contributing to these differences. When several artificial mixtures of PVC and poly(MVB) were analyzed by the method used to provide the data in the last column of Table I, the results in Table I11 were obtained. The arithmetric average of deviations of the found from the calculated chlorine contents, ignoring sign, was 1.6%. If all the data in the last column of Table I were lower by l.S%, the com-

REACTIVITY RATIOS 475

TABLE I11 Chlorine Analysis of Artificial Mixtures of Vinyl Chloride

and 2-Methylpentyl Vinyl Brassylate Homopolymers

PVC in mixtures

Mole C1 calcd, C1 found, PVC found, Deviation, Wt-% fraction % % Wt-% %

1.95 0.10 1.11 1.11 1.95 0 5.41 0.24 3.07 3.16 5.57 +2.93

13.56 0.47 7.69 7.97 14.05 +3.64 28.91 0.70 16.40 16.49 29.07 +0.55 46.52 0.83 26.39 26.71 47.08 +1.21

100.00 1.00 56.73 56.02 98.76 -1.25

a PVC, poly(viny1 chloride).

puted reactivity ratios in the last row of Table I1 would be r1 = 1.02 and r2 = 0.243. Similarly, if all the chlorine analyses were 1.6% higher, we would then have rl = 1.20 and rz = 0.235. The resulting spread of values of r1 and r2 arising from analytical errors is greater than the corresponding spread in Table 11. Admittedly, i t is unlikely that all experimental errors will be in the same direction, but four out of six analytical results listed in Table I11 are high and only one is low. A similarly unsymmetrical distribution of errors in chlorine contents determined for the copoly- mers in Table I could readily account for the difference in r1 and 7-2 values in Table 11.

We did not perform the experiment for differential refractometry analo- gous to the investigation of chlorine analysis represented in Table 111. However, it is reasonable to assume that experimental error in this method also contributed to differences in reactivity ratios computed from the two sources of data.

Table IV shows a comparison of results given by the computerized linear least-squares method for calculating reactivity ratios with resulk derived from the same experimental data by other mathematical proce- dures. Differences are of the same order of magnitude as those which may arise from experimental deviations such as shown in Table 111. Moreover, even greater experimental errors may result from the fractionation (i.e., loss of relatively small polymeric molecules) associated with isolation of copolymer samples for analysis. We believe, therefore, that the simple and convenient computerized 1inea.r least squares method gives rl and r2 with as much mathematical accuracy as is warranted in view of uncertainties inherent in the experimental data.

Wit.h regard to prediction of the comonomer distribution resulting from VC-MVB copolymerizations, rl is near unity, so a polymer chain with a VC radical a t the growing end is apt to react equally with VC or MVB. On the other hand, when an MVB radical occupies the growing end the likeli- hood of reaction with VC is much greater than with MVB according to the r2 value of 0.234-0.239. The relatively large difference between el (*0.20)

476 S.-P. CHANG, T. K. MIWA, W. H. TALLENT

TABLE IV Comparison of Different Methods for Calculating Reactivity Ratios

Source Monomer 1 Monomer 2 Methoda 1-1 r2 of data

Unidentified UnidentSed A 0.18 0.49 Ref. 15

vc Methyl acrylate A 0.0908495 10.065542 Ref. 16

Acrylonitrile Styrene A 0.067 0.37 Ref. 17

vc MVB A 1.23998 0.218459 Table I

vc Vinyl levulinate C 1.40 0.419 Ref. 18

vc Vinyl pelargo- C 1.16 0.282 Ref. 18

B 0.18 0.49

B 0.083 8.93

B 0.064 0.34

B 1.06 0.234

B 1.40 0.418

nate B 1.12 0.293

B 1.41 0.411

B 0.76 0.51

vc Vinyl pinonate C 1.46 0.446 Ref. 18

Methyl acrylate Acrylonitrile D 0.71 0.50 Ref. 19

a Method A = computerized nonlinear least-squares method of Tidwell and Mortimer. Values of rl and r2 by method A for the unidentified and for the acrylonitrile-styrene systems were taken from graphs.16 Dr. Mortimer graciously provided the ratios com- puted by method A from our differential refractometry data. Method B = computer- ized linear least-squares method with r1 given by slope of eq. (3) and rz given by slope of eq. (4). Method C = intersection method (graphic).e Method D = intersection method (algebrai~).’~

and ez (-0.95 to -0.98) favors monomer alternation,20 so formation is unlikely of blocks of monomers that would probably limit internal plastici- zation and otherwise adversely affect copolymer properties. Finally, the so-called “compositional drift” was calculated from the copolymer con- taining 60% VC by weight, the composition which produced plasticized products with the most promising mechanical properties of the several VC-iYVB copolymer samples investigated.2 The interquartile range found was 1.3y0 by graphic solution or 1.4y0 by the Meyer-Lowry solution to the Skeist equation, indicating that the plasticizing groups of the MVB will be homogeneously dispersed throughout the product.

We express our appreciation to E. B. Lancaster and J. 0. E m t for assistance in com- puter programming, C . E. McGrew and B. R. Heaton for chlorine analyses, W. F. Kwolek for reviewing the manuscript and offering helpful suggestions; also, G. A. Mortimer of the Monsanto Company, Texas City, Texas, for thought-provoking die cussions.

Reference to commercial products does not imply endorsement by the United States Department of Agriculture over similar products not mentioned.

References 1. S.-P. Chang, T. K. Miwa, and I. A. Wolff, J . Polym. Sci. A-l,5,2547 (1967).

REACTIVITY RATIOS 477

2. T. K. Miwa, S.-P. Chang, W. H. Tallent, I. A. Wolff, W. E. Palm, and L. P. Witnauer, paper preaented to the Division of Polymer Chemistry, American Chemical Society Meeting, 1967; Preprints, 8, No. 2,927 (1967).

3. F. W. Billmeyer, Jr., Textbook of Polymer Science, Interscience, New York, 1962, p. 312.

4. D. C. White, Mikrochim. Acfu, 1962,807. 5. J. B. Kinsinger, J. S. Bartlett, and W. H. Rauscher, J . Appl. Polym. Sci., 6, 529

6. F. R. Mayo and F. M. Lewis, J . A m . Chem. Soe., 66,1594 (1944). 7. M. Fineman and S. D. Ross, J . Polym. Sci., 5,259 (1950). 8. W. J. Youden, Statistical Methods for Chemists, Wiley, New York, 1951, p. 42. 9. R. W. Tess and W. T. Tsatsos, paper presented to the Division of Organic Coatings

and Plastics Chemistry, American Chemical Society Meeting, 1966; Preprints, 26, No. 2, 276 (1966).

(1962).

10. L. J. Young, J . Polym. Sci., 54,411 (1961). 11. I. Skeist, J. Amer. Chem. SOC., 68, 1781 (1946). 12. V. E. Meyer and G. G. Lowry, J . Polym. Sci. A , 3,2843 (1965). 13. J. R. Urwin and J. M. Stearne, Makromol. Chem., 78,204 (1964). 14. M. B. Huglin, J . Appl. Polym. Sci., 9,4003 (1965). 15. P. W. Tidwell and G. A. Mortimer, J . Polym. Sn’. A , 3,369 (1965). 16. E. C. Chapin, G. E. Ham, and R. G. Fordyce, J . Amer. C h . Soc., 70, 538

17. B. R. Thompson and R. H. Raines, J. Polym. Sci., 41,265 (1959). 18. C. S. Marvel and W. G. DePierri, J . Polym. Sci., 27,39 (1958). 19. R. M. Joshi and S. L. Kapur, J . Polym. Sci., 14,508 (1954). 20. T. Alfrey, Jr. and L. J. Young, in Copolymerization, G. E. Ham, Ed., Interscience,

(1948).

New York, 1964, p. 67.

Received March 26, 1968 Revised May 28, 1968